Aggregation functions on the set of discrete fuzzy numbers defined from a pair of discrete aggregations

Abstract In this paper we propose a method to construct aggregation functions on the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers from a couple of discrete aggregation functions. The interest on these discrete fuzzy numbers lies on the fact that they can be interpreted as linguistic expert valuations that increase the flexibility of the elicitation of qualitative information based on linguistic terms. Finally, a linguistic decision making model based on a pair of aggregation functions defined on discrete fuzzy numbers is given.

[1]  Da Ruan,et al.  A fuzzy-set approach to treat determinacy and consistency of linguistic terms in multi-criteria decision making , 2007, Int. J. Approx. Reason..

[2]  Etienne E. Kerre,et al.  Aggregation Operators in Interval-valued Fuzzy and Atanassov's Intuitionistic Fuzzy Set Theory , 2008, Fuzzy Sets and Their Extensions: Representation, Aggregation and Models.

[3]  Vicenç Torra,et al.  Modeling decisions - information fusion and aggregation operators , 2007 .

[4]  Bernard De Baets,et al.  Idempotent uninorms on Finite Ordinal Scales , 2009, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[5]  Vicenç Torra,et al.  On aggregation operators for ordinal qualitative information , 2000, IEEE Trans. Fuzzy Syst..

[6]  Imre J. Rudas,et al.  Uninorms and Absorbing Norms with Applications to Image Processing , 2006 .

[7]  Gaspar Mayor,et al.  Aggregation Operators , 2002 .

[8]  Jaume Casasnovas,et al.  Extension of discrete t-norms and t-conorms to discrete fuzzy numbers , 2011, Fuzzy Sets Syst..

[9]  William Voxman,et al.  Canonical representations of discrete fuzzy numbers , 2001, Fuzzy Sets Syst..

[10]  Francisco Herrera,et al.  Hesitant Fuzzy Linguistic Term Sets for Decision Making , 2012, IEEE Transactions on Fuzzy Systems.

[11]  Joan Torrens,et al.  Aggregation of subjective evaluations based on discrete fuzzy numbers , 2012, Fuzzy Sets Syst..

[12]  R. Mesiar,et al.  Aggregation Functions (Encyclopedia of Mathematics and its Applications) , 2009 .

[13]  Jaume Casasnovas,et al.  Lattice Properties of Discrete Fuzzy Numbers under Extended Min and Max , 2009, IFSA/EUSFLAT Conf..

[14]  M. K. Luhandjula Studies in Fuzziness and Soft Computing , 2013 .

[15]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[16]  Francisco Herrera,et al.  Linguistic decision analysis: steps for solving decision problems under linguistic information , 2000, Fuzzy Sets Syst..

[17]  Humberto Bustince,et al.  A gravitational approach to edge detection based on triangular norms , 2010, Pattern Recognit..

[18]  Jaume Casasnovas,et al.  Maximum and Minimum of Discrete Fuzzy Numbers , 2007, CCIA.

[19]  R. Mesiar,et al.  Aggregation operators: new trends and applications , 2002 .

[20]  Humberto Bustince,et al.  An alternative to fuzzy methods in decision-making problems , 2012, Expert Syst. Appl..

[21]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[22]  V. Torra,et al.  A framework for linguistic logic programming , 2010 .

[23]  R. Yager Using importances in group preference aggregation to block strategic manipulation , 2002 .

[24]  Etienne E. Kerre,et al.  On the relationship between some extensions of fuzzy set theory , 2003, Fuzzy Sets Syst..

[25]  Francisco Herrera,et al.  Fuzzy Sets and Their Extensions: Representation, Aggregation and Models , 2008 .

[26]  R. Mesiar,et al.  Aggregation Functions: Aggregation on ordinal scales , 2009 .

[27]  Yongchuan Tang,et al.  Linguistic modelling based on semantic similarity relation among linguistic labels , 2006, Fuzzy Sets Syst..

[28]  Radko Mesiar,et al.  Triangular norms on product lattices , 1999, Fuzzy Sets Syst..

[29]  G. Mayor,et al.  Triangular norms on discrete settings , 2005 .

[30]  Ronald R. Yager,et al.  Defending against strategic manipulation in uninorm-based multi-agent decision making , 2002, Eur. J. Oper. Res..

[31]  Mariano Eriz Aggregation Functions: A Guide for Practitioners , 2010 .

[32]  Radko Mesiar,et al.  Weighted ordinal means , 2007, Inf. Sci..

[33]  Ramon E. Moore Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[34]  G. Mayor,et al.  t‐Operators and uninorms on a finite totally ordered set , 1999 .